So, I’ve been doing a little research in elevators and such, and given the recent RAMP video, this sparked a little bit of interest (which lead to confusion) about some of the finer details about elevator systems.

For continuous elevators, why is it that one of the drums needs to be twice the size of the other (if the system is powered up and down)?

For cascade systems, I’m a little perplexed as to how the cascade affects the forces and speeds of the elevator. On some CD posts, they say that you need more force to power a cascade system?

I’d appreciate any input,

• Sunny G.
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Let’s imagine a 2 (moving) stage elevator.

Continuous means you have a single cable that runs through every stage. Whel you pull on it, you’ll (usually) have just the smallest stage moving (the one your mechanism is attached to, holding the game piece). Pull up 4 ft, and that stage moves up 4 ft until it hits the top. At this point, that stage is motionless, relative to the next stage. That next stage then starts moving, and if you pull another 4 ft, you get 4 more ft of movement. So in the end, 8 ft of pull gets you 8 ft of movement.

Thus, continuous results in the same size spindle for both up and down.

Cascade is a little different. The wire from the motor hooks on the outer stage, while the inner stage has a wire that goes over the outer stage to attach to a fixed point. So, when you pull on the wire, you start moving the outer stage, which also moves the inner stage. As a result, pulling 4 ft of wire pulls the outer stage up 4 ft, and the inner stage up 4 ft relative to the outer stage - 8 ft total. As a result, to power it down your spindle needs to be twice as big to give you twice the distance for the same rotation.

Now, for speed. In continuous, we saw that 1 ft pulled = 1ft moved. In cascade, 1 ft pulled = 2 ft moved. So, cascade moves twice as fast as continuous, assuming equal gear ratios, drum sizes, motors, and required force for lifting.

Now for force… This is where it gets tricky (and where I wish I wasn’t on my ipad so I could draw a free body diagram for you). The inner most stage has a weight of w1. The outer stage has a weight of w2.

In continuous, your pulling up w1+w2. Pretty simple.

In cascade, you directly pull up w2. However, since the inner stage is affixed over the outer stage and attached to a fixed point, you end up doubling the weight. Think of it like this: the inner stage pulls down w1 AND the fixed point pulls down w1, otherwise he inner stage wouldn’t stay up. Thus the outer stage has to pull up 2 x w2. So overall your pulling up w1+2 x w2. Essentially, you’re doubling the weight of your game piece to lift it!

To put all of this in perspective, my team built two elevators in separate years. For Overdrive, we had a continuous elevator. It was slow, but had no problem picking up a trackball. For LogoMotion we had a cascade. It was very fast, and had no problem picking up an innertube, although I doubt it could have picked up the trackball. They were both powered by a fisher price motor through the FP gearbox.

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The force difference between continuous and cascade is simplest to understand if you just think of it as exactly like a gearing system. If, in the continuous system, 1ft in = 1ft out, then that’s like a 1:1 gear ratio. In the cascade, 1ft in = 2ft out. That’s a 1:2 gear ratio. WorkIn = WorkOut, so ForceDist In = ForceDist Out. Your output is moving twice as far, so it can apply half the force that you apply at the input. If you’re lifting the same weight, that means twice the force in.

Really, an awful lot of the simple machines come down to WorkIn = WorkOut. The only tricky part is figuring out how you correctly calculate work for a given device/motion. Converting ball screw pitch into torque to apply X force is always a good one, for instance.

To solve for the forces/speed of elevator, look no further than reducing everything to free body diagram(s). Remember in a free body diagram we want everything to equal zero in static calculations (which we have simplified this to). We are neglecting the weight of the elevator parts in these diagrams. Also, we are assuming all rope forces are perfectly vertical (which they should be if you designed the elevator right).

Continuous:
The free body diagram of continuous elevators are relatively simple; the cable in this effectively just keeps toggling the weight on the end of the elevator up and down again. I broke this down into three notes, N1, N2, N3.

Node 1 is the top pulley of the second stage, Node 2 is the bottom pulley of the second stage, and Node 3 is the top pulley of the first (fixed stage).

Node 1 sees the weight on the end of the elevator, expressed as W. Both sides of a cable around a pulley see identical force. The position of the elevator is static, so the cable itself must exert equal and opposite forces, which means they both point down (since the cable is curved around a pulley with 180 degrees of wrap). To keep the node static, the pulley exerts a +2W to counter-act the -2W force exerted by both sides of the cable.

Node 2 is the equal and opposite version of Node 1, and Node 3 is the equal and opposite of Node 2 (and identical to Node 1). The weight of the elevator load travels entirely through the rope, and at any given point in the cable the magnitude of the force is always equal to exactly W, no more, no less. Note in this version the +2W and -2W forces are entirely internal (they only apply to the fixed members inside the elevator).

Thus, the cable at the motor sees a force equal to that weight of the object, and the object travels upward at a 1:1 rate compared to how much the cable is pulley.

Cascade is a bit different. Because there are multiple cables, we are not guaranteed the same force in the cable at any given point. So we need to be more careful with this version on setting up the FBD correctly. Here is the drawing:

Node 1 starts the same as continuous, with two separate -W forces and one +2W force inside the second stage beam. But Node 2 is where things change.

Node 2 does not see any direct rope forces from Node 1; the rope from Node 1 is tied to a fixed point on the first stage. Node 2 sees the internal force of the second stage fixed member, then uses the second rope force to equalize this. The -2W force is the equal and opposite force to the +2W force seen in Node 1 transmitted through the rigid elevator member. To keep this node static, we need the cable to Node 3 to transmit a +2W force.

Node 3 is contains the -2W cable force from Node 2 which also means a 2W force going to the motor, which means we need a total of +4W vertical force (1W of this force will be from the cable from Node 1) at the pulley to counter act it.

Thus, the cable at the motor sees 2x the weight of the object. But for every centimeter that the second stage is directly pulled upwards by the motor, the third stage carriage moves up at 2x this rate.

All said and done, these both use the same motor mechanical power to move the final (third) stage. Using continuous as a baseline, cascade requires 2x the torque at the input, but only requires half the input speed to make the output stage move at the same rate*.

• These only hold true if there are two moving stages.

Could someone (Adam?) go into a bit more detail about rigging the cabling in an elevator? For example, what type of cable is best, how do you deal with tensioning and stretching, and how do you tie it off the best? What are good ways to attach the cable to the drum, how do you keep it from getting tangled, and what are good ways to do pulleys?

I’m also not 100% clear on how to do the Constant Force Springs. What’s the best way to mount a CFS, and what are some of the better suppliers for CFSes? Also, I’ve had mentors try to dissuade me from using a CFS because it’s basically a razor blade under 40 lbs of tension. Are CFSes safe to use, and what’s some advice about setting them up safely?

I don’t have recent experience, but I do have a few answers.

Generally, my experience is with wire rope. It’s strong, and if you get it coated, it’s pretty smooth. It can be tied off by using a thimble or simply creating a loop, or if you happen to have 3 holes, weave it through them and pull tight (best on the drum, mind you). Take a look at McMaster. BTW, if you’re planning to use compression sleeves to create your loops, do yourself a favor and get the proper crimpers–the “vice or pliers” method could fail. I’ve even seen a poorly done standard crimp fail–one of mine, to be exact.

Tensioning is actually pretty easy if you have a turnbuckle. Running a tight cable generally will prevent tangling; the turnbuckle, when turned, keeps the cable tight. (NOT on the drum end, though!)

I know Spectrum 3847 ran a good elevator last year. Maybe Allen can post some details about theirs.

The last time I designed a real elevator was in 2011 when I was a college mentor for 228. My main goal was a really fast (<2 sec) and reliable lift, so I chose to avoid drums altogether. There are a bunch of photos of this setup online here: http://team228.org/media/pictures/2011/build-season-week-six

I used fixed loops of 25p roller chain that I interspaced tension springs into to maintain tension in the chain due to stretching/wearing in. Make sure all the tension springs work on the downward pull, because if they work on the upward stroke you might get a slingshot effect (we learned this one the hard way). On a really fast elevator, the tension spring will stretch before the inertia of the carriage gets moving, so it will then slingshot upwards. If you put it on the downward stroke, gravity helps prevent this slingshot effect.

To fix the roller chain to the elevator stages, I simply ran #4-40 bolts through the holes in the roller chain.

You do have to be careful with CF springs, but if used properly they work great. To use them just bolt the end with the mounting holes to your object then provide a loose clearance fit inside the spool on the other side. I’m pretty sure last time I used them I used a piece of 1" ish PVC pipe to act as the internal bushing for the curling half of the CF spring. Just let this side free spin on the ID.

Be careful with elevators with CF springs when in the pits. If you balance the elevator right, when you tip the robot sideways to work on it, the lack of gravity fighting the CF springs will cause the elevator to shoot outwards to fully elevated. Which when sideways, means you may hit someone standing several feet away.

As for a source, I’ve always used McMaster. Also, avoid kinking them at all costs, as you may begin to tear through the spring if you bend/kink it.

On another note, do you think that one or two of these would be able to hold the weight of the elevator, if I wanted to use 15mm wide 5mm HTD belts? I’m interested in using a belt to drive the first stage (IE, the larger frame that moves) with a steel cable to run the second stage (or carriage) in a two stage, cascaded setup.

We used 1/16" steel cable in 2007. It sucks. working with it is miserable. You will end up with bloody fingers every time you touch it.

Since then we’ve used Dyneema. It is tremendously strong (used in sailing), lighter, and easier to work with. There is a certain type of knot that you have to use to avoid reducing the strength of the line dramatically at the knot. I don’t remember what knot that is, but someone else may be able to chime in here.

In a continuous elevator you want to mount it to the carriage with some kind of spring element (we’ve used springs, or bungee cords, but a bungee cord doesn’t last very long).

For attaching to the spool I want to say we tied a loop in the end of the line, big enough for a 10-32 screw to pass through, which we screwed into a drilled/tapped hole in the plug holding the two spool halves together…but my memory isn’t that great.

We’ve never had an issue with tangling and don’t do anything special to avoid it.

Constant force springs aren’t dangerous until you load them out of axis or try to unroll them a little to made the ID fit something not quite nominal. If you do, you’re asking for them to unwind and cut you. It’s happened to us once and it wasn’t pretty.

You can find a lot of info about counterbalancing (and some detailed pics of our elevator) here

There are other interesting ways of doing elevators that are quite elegant such as 971’s use of belts.

That’s probably a bowline (“bolun”). It’s used extensively in sailing because of its strength and ease of untying, however all knots will reduce the strength of the line significantly. A splice however, can retain up to 80%-90% of the line strength. Given the strength of dyneema though, you could probably still have a good safety margin for an elevator even with 30% of the breaking strength, due to knots.

Dyneema is great stuff, highly recommended.

Just wondering, is this the same as Spectra cable, or is it a different material?

We used the steel cable up through 2008. In 2011, we used Dyneema. We also used the Dyneema in our kicker winch in 2010.

If I remember correctly, the knot we’ve had the best luck with is the triple fisherman’s knot. The bowline tended to slip under load.

In 2011, we did have some issues with the Dyneema jumping off of its pulleys and getting wedged in to the pulley mount blocks. We fixed this by dramatically reducing the amount of clearance between the pulleys and the mounts (down to ~.015" IIRC).

Dyneema and Spectra are similar and are both made of UHMW. We used Dyneema because it was easier to source in the diameters we needed (West Marine).

Nylon webbing is another good option for these sorts of applications. 1114 used it on their 2010 kicker and 2011 cascading elevator.

Ah, that’s exactly what I needed. Thanks for drawing those out, and I see where I messed up on my own diagrams.

If you look at RAMP’s latest videos, there’s one that goes into detail about elevator rigging and such. There’s a video coming that’s going show the elevator rigged with #25 chain. Although, if you have a request for more detail, perhaps send a message directly to Adam Heard or the 973 Ramp youtube account.

In the past, my team has used whatever pulleys are available on McMaster. If you want to go custom, you can purchase the pulleys and then make your custom brackets and everything, but for us, it was easier to go COTS for the entire assembly.

Oh, so, I see. I suppose cascade has two variants: one where each stage is powered with a closed loop and one where the loop is closed when the carriage is attached back to the “spindle.” That makes a ton more sense.

• Sunny G.